In general, stress distribution is utilized to discuss the behavior of the load transfer in the structural object. However, a stress-concentrated point is not always the transfer point of force. The point that stress is concentrated locally is sometimes connected weakly with the loading point. Therefore, the connective stiffness in relation to the loading point cannot be obtained from the stress concentration. Then, the present inventors proposed the new parameter U* able to indicate clearly the force transfer in the patent document 1 and the non-patent documents from 1 to 9. The parameter U* is the parameter to show the connective stiffness in relation to the loading point with respect to arbitrary point in the structural object and to indicate the behavior of the load transfer.
The parameter U* is calculated based on the concept of “displacement method.” One point in the structure is fixed and the displacement is given to the loading point. And then, the value of the parameter U* can be calculated. The force flow or the load transfer can be naturally represented with the stiffness from the loading point. The structure is designed from this viewpoint. The parameter U* represented with the stiffness matrix can be rather grasped intuitionally than the stress distribution. The design method utilizing the parameter U* is employed actually in the automobile manufacturers. The problems of the chassis and body are found by examining the load transfer path and then the reinforcement of stiffness is considered. It is confirmed that the parameter U* is very useful in this field. For the detail of the parameter U*, the patent document 1 and the non-patent documents from 1 to 9 can be referred to as shown in the following with their abstracts.
The numerical structure analysis system as disclosed in the patent document 1 is the system able to reduce the calculation time based on load transfer method. The parameters are set in the condition that the supporting point B in the objective structure is fixed and the load is applied to the specific loading point A. The FEM calculation means calculates the deformation of the objective structure according to the total stiffness matrix in the stiffness matrix holding means to find the basic data such as the displacement of each point and so on. The FEM calculation means calculates each deformation to find the displacement under the condition that the specific loading point A and the supporting point B are fixed and three inspection loadings are applied to the variable loading point C. The partial stiffness matrix calculation means solves the multidimensional simultaneous linear equation based upon the inner stiffness matrix of the objective structure, the load value and the displacement to find the partial stiffness matrix KAC. The stiffness parameter calculation means calculates the value of the stiffness parameter U* according to the partial stiffness matrix KAC and the displacement in the basic data and so on. The value of U* of each point is calculated while changing the variable loading point C so that all the necessary points in the objective structure may be followed sequentially.
In the non-patent document 1, conditions for desirable structures based on a concept of load transfer courses is reported. A new concept of a parameter E is introduced to express load transfer courses for a whole structure. A degree of connection between a loading point and an internal arbitrary point in the structure can be quantitatively expressed with the parameter E. Based on the proposed concept, three conditions for desirable structures are introduced: (1) Continuity of E, (2) Linearity of E, (3) Consistency of courses. After introducing these three conditions as objective functions, structural optimization with numerical computation is carried out. Despite the fact that no concept of stresses or strains is introduced, the obtained structure has a reasonable shape. Finally, the load transfer courses for a simple structure are experimentally measured and these values demonstrate that the parameter E can effectively be used.
In the non-patent document 2, vibration reduction for cabins of heavy-duty trucks with a concept of load path is reported. The load transfer paths in the cabin structures of heavy-duty trucks are investigated under static loading and the results are applied to the vibration reduction of cabins. In a preliminary simulation using a simple model, it is shown that the floor panel vibration is closely related to the stiffness of the front cross-member of the floor structure. Load path analyses using the finite element method show that the load paths have some discontinuities and non-uniformities in the front cross-member which cause the low stiffness of the member.
In the non-patent document 3, application of ADAMS for vibration analysis and structure evaluation by NASTRAN for cab floor of heavy-duty truck is reported. The load transfer paths in the cabin structures of heavy-duty trucks are investigated under static loading, and the results are applied to the reduction of vibration in cabins. In a preliminary simulation using a simple model with ADAMS/Vibration, it is shown that vibration in the floor panel is closely related to the stiffness of the front cross-member of the floor structure. Load path analyses using the finite element method with NASTRAN show that the load paths have some discontinuities and non-uniformities in the front cross-member, reducing that member's stiffness.
In the non-patent document 4, ADAMS application for the floor vibration in the cabin of heavy-duty trucks and U* analysis of the load path by NASTRAN is reported. Realization of lightweight and cost-effective structures of heavy-duty trucks is an important aspect of structural designs, and numerical analyses have played a key role in this regard. In a preliminary simulation using ADAMS/Vibration, it is shown that the floor panel vibration is closely related to the stiffness of the front cross-member. Load path analyses using MSC/NASTRAN show that the load transfer paths have some discontinuities and non-uniformities in the front cross-member.
In the non-patent document 5, expression of load transfer paths in structural analysis and its applications is reported. A new parameter U* is introduced to express the load transfer path using FEM. As an example, load path U* analysis is applied to a plate structure with a circular hole. Although the effect of stress concentration suggests strong force transfer at the corner of the hole, the obtained position of the load transfer path avoids a corner of the hole. This result coincides with their intuitive prediction. Moreover, they try to extend the calculation method of U* analysis to a structure with more complex boundary conditions. The effectiveness of the introduced method is verified using the FEM model of an actual heavy-duty truck cab.
In the non-patent document 6, load path optimization and U* structural analysis for passenger car compartments under frontal collision is reported. A new concept, a parameter U*, is introduced to express load transfer in a structure. Two cases of U* analysis for a floor structure of a passenger compartment are examined. In the first case, three conditions of U* are introduced as objective functions, and GA (Genetic Algorithm) structural optimization is applied. The emergent floor structure after the GA calculation has a unique shape in which a member connects the frontal part of an under-floor member and the rear part of a side-sill. In the second case, the U* values and the load paths in a floor structure under collision are calculated by use of PAM-CRASH. As the collision progresses, the under-floor member becomes the principal load path, and in the final stage of the collision the roll of the under-floor member becomes dominant.
In the non-patent document 7, vibration reduction in the cabins of heavy-duty trucks using the theory of load transfer paths is reported. The objective of this study is to investigate the load transfer paths in the cabin structures of heavy-duty trucks under static loading, and to apply the results to reduce vibration in cabins. In a preliminary simulation using a simple model, it is shown that the floor panel vibration is closely related to the stiffness of the front cross-member of the floor structure. Load path U* analyses using the finite element method show that the low stiffness of the front cross-member is caused by discontinuities and non-uniformities in the load paths.
In the non-patent document 8, expression of load transfer paths in structures is reported. A concept of a parameter U* has been introduced by the authors to express load transfer paths in a structure. In this paper, matrix formulation of internal stiffness shows that the value of U* expresses a degree of connection between a loading point and an internal arbitrary point. Stiffness fields, stiffness lines, and stiffness decay vectors are defined using newly introduced U* potential lines. A concept of a load path can be expressed as a stiffness line that has a minimum stiffness decay vector. A simple model structure is calculated using FEM for an application of U* analysis. The distribution of U* values shows that a diagonal member between a loading point and a supporting point plays an important role for the load transfer.
In the non-patent document 9, experimental study of U* analysis in load transfer using the actual heavy-duty truck cabin structure and scaled model is reported. The distribution of U* is known to indicate the load transfer path in the structure. Two experimental measuring method of U* is developed of U* with respect to the actual heavy-duty truck cabin structure and the scaled plastic model. In these methods, different from the conventional method, the stiffness data of each member is not necessary. In FEM, the effect of the actual plate to play the important role in U* analysis cannot be expressed. By using the plastic scaled model, the strengthening effect can be directly measured according to the distribution of U* value.    Patent document 1: JP2005-321695(Application Specification)    Non-patent document 1: Kunihiro Takahashi; Conditions for desirable structures based on a concept of load transfer courses, International Structural Engineering and Construction Conference (ISEC-1) Honolulu, Proc. ISEC-01, pp. 699-702, 2001.    Non-patent document 2: Toshiaki Sakurai, Hiroaki Hoshino, Kunihiro Takahashi; Vibration Reduction for Cabins of Heavy-Duty Trucks with a Concept of Load Path, Proc. JSAE No. 36-02, pp. 5-8, 2002 (in Japanese with English summary).    Non-patent document 3: Hiroaki Hoshino, Toshiaki Sakurai, Kunihiro Takahashi: Application of ADAMS for Vibration Analysis and Structure Evaluation By NASTRAN for Cab Floor of Heavy-Duty Truck, The 1st MSC.ADAMS European User Conference, London, November, 2002.    Non-patent document 4: Toshiaki Sakurai, Hiroaki Hoshino, Masatoshi Abe, Kunihiro Takahashi; ADAMS Application for the Floor Vibration in the Cabin of Heavy-duty Trucks and U* Analysis of the Load Path by NASTRAN, (MSC.ADAMS User Conference 2002).    Non-patent document 5: Toshiaki Sakurai, Masatoshi Abe, Soei Okina, Kunihiro Takahashi; Expression of Load Transfer Paths in Structural Analysis and its Applications, Trans. JSCES, Vol. 8, pp. 401-404, May 2003.    Non-patent document 6: Toshiaki Sakurai, Junichi Tanaka, Akinori Otani, Changjun Zhang, Kunihiro Takahashi; Load Path Optimization and U* Structural Analysis for Passenger Car Compartments under Frontal Collision, International Body Engineering Conference 2003, pp. 181-186, JSAE 20037007, SAE 2003-01-2734, 2003.    Non-patent document 7: Hiroaki Hoshino, Toshiaki Sakurai, Kunihiro Takahashi: Vibration reduction in the cabins of heavy-duty trucks using the theory of load transfer paths, JSAE Review 24(2003) 165-171.    Non-patent document 8: Kunihiro Takahashi, Toshiaki Sakurai: Expression of Load Transfer Paths in Structures, J. JSME, (A)71-708 (2005), pp. 1097-1102.    Non-patent document 9: Kengo Inoue, Yuichiro Ichiki, Ikuma Matsuda, Toshiaki Sakurai, Hideaki Ishii, Tetsuo Nohara, Hiroaki Hoshino, Kunihiro Takahashi: Experimental study of U* analysis in load transfer using the actual heavy-duty truck cabin structure and scaled model, Proc. JSAE, No. 90-04, pp. 27-30, 2004.